Topics covered include the Monte Carlo simulation (including simulation of random variables, variance reduction, quasi-Monte Carlo simulation, and more recent developments such as the multilevel paradigm), stochastic optimization and approximation, discretization schemes of stochastic differential equations, as well as optimal quantization methods. The author further presents detailed applications to numerical aspects of pricing and hedging of financial derivatives, risk measures (such as value-at-risk and conditional value-at-risk), implicitation of parameters, and calibration.

Aimed at graduate students and advanced undergraduate students, this book contains useful examples and over 150 exercises, making it suitable for self-study.

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Gilles Pag�s is full Professor of Mathematics at Sorbonne Universit� (formerly Universit� Pierre & Marie Curie) specializing in probability theory, numerical probability and mathematical finance. He was the director of the Laboratoire de Probabili�ts & Mod�les A�atoires (now Laboratoire de Probabilit�s, Statistique et Mod�lisation) from 2009 to 2014, and has been the director of the Master 2 "Probabilit�s & Finance", also known as "Master ElKaroui", since 2001. He has published over 100 research articles in probability theory, numerical probability and financial modelling. He is also the author of several graduate and undergraduate textbooks in statistics, applied probability and mathematical finance.

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